Wireless position sensing using magnetic field of two transmitters

ABSTRACT

A positioning system for determining the location of a receiver relative to a transmitter. The system includes two transmitting coils configured to transmit a periodic signal with a respective selected frequency during a positioning event, wherein the frequencies of the two signals transmitted by the two transmitting coils during the positioning event are different. A receiver includes a sensing unit for measuring the magnetic field vectors produced by the two simultaneously transmitting coils. A computing unit is configured to use the measured magnetic field vectors to calculate the position and orientation of the receiver with respect to the transmitter&#39;s coordinate frame.

RELATED APPLICATIONS

The present application claims the benefit of U.S. provisional application Ser. No. 61/984,242, filed Apr. 25, 2014, the contents of which are hereby incorporated by reference in its entirety.

TECHNICAL FIELD

The present application relates to wirelessly detecting positions of devices, e.g., portable or mobile devices.

BACKGROUND

There is an increasing need for ways of determining the location of mobile or portable objects or devices, e.g., cellular telephones or blood-borne sensors. GPS, LORAN, and similar systems can provide location information, but often only with resolution on the order of 15 m. Moreover, such systems can be more difficult to use indoors due to changes in signal propagation through walls and other features of buildings. WIFI or BLUETOOTH triangulation has been proposed and may have an accuracy as low as 1-2 m indoors. However, these schemes often require large databases of known transmitters (TX). There is, therefore, a need of positioning systems that provide high accuracy and do not require large databases.

Reference is made to US 2013/0166002 by Jung et al., published Jun. 27, 2013, the disclosure of which is incorporated herein by reference.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features, and advantages of the present invention will become more apparent when taken in conjunction with the following description and drawings wherein identical reference numerals have been used, where possible, to designate identical features that are common to the figures, and wherein:

FIG. 1 is a simplified block diagram of a positioning system according to one embodiment.

FIG. 2 is a block diagram showing the system of FIG. 1 in a 3-dimensional environment.

FIG. 3A is a simplified block diagram illustrating envelope detection using a computing unit according to one embodiment.

FIG. 3B is a simplified block diagram illustrating envelope detection using an analog envelope detector according to one embodiment.

FIG. 4 is a plot showing a predicted field model for a single coil according to one embodiment.

FIG. 5 is a plot showing a predicted field model for two coils according to one embodiment.

FIG. 6 is a simplified block diagram of a positioning process according to one embodiment.

FIG. 7 is a diagram showing an example experimental setup of the system of FIG. 1.

FIG. 8 is a flowchart illustrating a positioning process according to one embodiment.

The attached drawings are for purposes of illustration and are not necessarily to scale.

DETAILED DESCRIPTION

In the following description, some aspects will be described in terms that would ordinarily be implemented as software programs. Those skilled in the art will readily recognize that the equivalent of such software can also be constructed in hardware, firmware, or micro-code. Because data-manipulation algorithms and systems are well known, the present description will be directed in particular to algorithms and systems forming part of, or cooperating more directly with, systems and methods described herein. Other aspects of such algorithms and systems, and hardware or software for producing and otherwise processing the signals involved therewith, not specifically shown or described herein, are selected from such systems, algorithms, components, and elements known in the art. Given the systems and methods as described herein, software not specifically shown, suggested, or described herein that is useful for implementation of any aspect is conventional and within the ordinary skill in such arts.

Various aspects herein advantageously permit position to be determined rapidly using a low-power microcontroller. No large database of hotspots or antennas is required. Various aspects permit very high-speed tracking of motion.

Throughout this disclosure, the term “coil” when used in reference to an antenna is not limiting, and other types of antennas capable of performing the listed functions can be used. Various aspects herein use low frequencies, e.g., <1 MHz or <500 kHz, ˜70 kHz, or ˜80 kHz or ˜35kHz. Other frequencies can also be used, e.g., >1 MHz. Magnetic sensors described herein can include sensors including two or more substantially orthogonal coils for measuring components of a magnetic field. A triaxial or other magnetoresistive sensor can also or alternatively be used.

Throughout this disclosure, references to the Earth's coordinate system include other reference coordinate systems common or substantially common to transmitter and receiver.

In one embodiment, an approximate location can be used as a starting point to locate the magnetic-field vector of interest. Initial estimates of the approximate location can be made in various ways. The approximate location is within an area determined using the determined signal strengths (magnetic field strengths) of the arriving signals and a corresponding estimate of distance to each transmitter (as in distance estimation using WiFi, Bluetooth, RFID signal strength).

In one example, an exhaustive search is performed of coarsely-spaced sample points in the search area. More closely-spaced sample points are then tested around the coarsely-spaced point that gives the minimum error. This procedure is repeated with successively more closely-spaced sets of sample points (successively finer sampling grids) until the required spatial accuracy is satisfied.

Throughout this disclosure, once a position or orientation of the receiver is determined with respect to the transmitter, that position or orientation can be transformed into other coordinate systems, e.g., Earth-relative systems such as WGS84 or local systems such as a coordinate frame of a room or building. Coordinate transforms can be done using rotations, skews, and other techniques well known in the computer-graphics and cartographic arts.

In view of the foregoing, various aspects providing determination of the location of a receiver in proximity to a wireless transmitter are disclosed. A technical effect is to detect magnetic fields from the transmitter(s) and determine the location of the receiver using the detected fields. Further technical effects of various aspects include presenting an indication of the receiver's position on an electronic display and transmitting the determined position to the transmitter, a computer or computing unit, or another device.

FIG. 1 illustrates a basic block diagram of a positioning system 100 according to one embodiment. As shown, the positioning system 100 includes two transmitters (shown as antenna coils 102) and at least one receiver 104. The receiver 104 includes a tri-axis magnetic sensor 106. The coils 102 are placed in different positions and can have any two-dimensional and three-dimensional shape: circular, elliptic, rectangle, square, diamond, triangle, etc. Signal generator 110 and drivers 112 may be included to generate waveforms and drive the coils 102 simultaneously to transmit periodic beacon signals which have a fixed frequency. Any periodic signal can be used, but a sinusoidal signal is preferred as it is most effective for simplifying the transmitter and receiver design. The frequencies f1 and f2 of the two periodic signals from the two transmitting coils are close to each other but different. Preferably, f1≠f2, |f1−f2|<f1/10, and |f1−f2|<f2/10.

The transmitting coils 102 will generate a spatial magnetic field where the field strength and direction depends on the position in the space. Because the two signals from the two transmitters have slightly different frequencies, the amplitude of the magnetic field signal at any given position (x, y, z) will be modulated where the modulation frequency is the difference between the two transmitting signal frequencies |f1−f2|.

Amplifiers 112, A/D converters 116 may be operatively connected as shown to amplify and convert the output of the magnetic sensor 106 to a digital form suitable for input by a computing unit 118.

FIG. 2 illustrates operation of the system 100 in a 3-dimensional environment. The tri-axis magnetic sensor 106 in the receiver 104 measures the signal transmitted by the two transmitting coils 102. In the illustrated embodiment, the sensor 106 may comprise three planar coils orthogonally placed relative to each other as a tri-axis magnetic sensor. In other embodiments, a solid state tri-axis magnetic sensor such as three orthogonally placed magnetoresistive sensors may be used as sensor 106. The computing unit 118 may be placed in the receiver 104, in the transmitter, or remoted located somewhere else. When the computing unit 118 is not placed in the receiver 104, the measured data may be sent to a remote computing unit placed outside of the receiver 104 through a wireless channel or wired channel.

As shown in FIG. 3, the envelope of the amplitude modulated signal 113 from the coils 102 may be detected using the computing unit 118 (FIG. 3A). Alternatively, the envelope detection may be performed by an analog envelope detector 115 connected to the sensor 106 (FIG. 3B).

By measuring the maximum and minimum values of the modulated signal,) we can estimate the magnetic field signal vectors (E_(u1), E_(v1), E_(w1)) and (E_(u2), E_(v2), E_(w2)) in the receiver 104 coordinate frame (U, V, W). The magnitudes of the two measured magnetic field signal vectors and the angle between the two vectors may be estimated using the following equations:

$\begin{matrix} {{{{E\; 1}} = \sqrt{E_{u\; 1}^{2} + E_{v\; 1}^{2} + E_{w\; 1}^{2}}}{{{E\; 2}} = \sqrt{E_{u\; 2}^{2} + E_{v\; 2}^{2} + E_{w\; 2}^{2}}}{\theta_{M} = {\arccos\left( \frac{{E_{u\; 1}E_{u\; 2}} + {E_{v\; 2}E_{v\; 2}} + {E_{w\; 1}E_{w\; 2}}}{\sqrt{E_{u\; 1}^{2} + E_{v\; 1}^{2} + {E_{w\; 1}^{2}\sqrt{E_{u\; 2}^{2} + E_{v\; 2}^{2} + E_{w\; 2}^{2}}}}} \right)}}} & (1) \end{matrix}$

The magnetic field vectors in the transmitter coils 102 coordinate frame (X, Y, Z) is still unknown. However, because the magnitude of a magnetic field vector measured by the receiver 104 at a given position must be the same regardless of the coordinate frame, we can show that:

|E1|=√{square root over (E_(u1) ² E+ _(v1) ² +E _(w1) ²)}=√{square root over (E _(x1) ² + E _(y1) ² +E _(z1) ²)}

|E2|=√{square root over (E_(u2) ² +E _(v2) ² +E _(w2) ²)}=√{square root over (E _(x2) ² +E _(y2) ² +E _(z2) ²)}  (2)

where (E_(x1), E_(y1), E_(z1)) and (E_(x2), E_(y2), E_(z2)) are the expected magnetic field vectors in the transmitter's coordinate frame (X, Y, Z), and (E_(u1), E_(v1), E_(w1)) and (E_(u2), E_(v2), E_(w2)) are the measured magnetic field vectors in the receiver's coordinate frame (U, V, W).

The following is a graphical explanation of the above method. FIG. 4 shows an equi-magnetic field magnitude surface 400 when one transmitting coil 102 transmits. When the transmitting coil 102 has a circular shape, the equi-magnitude surface 400 has an ellipsoid shape. We used a circular shaped transmitting coil 102 in this example for mathematical simplicity, but the transmitting coil can have any shape. Because we measure two magnetic field magnitudes from the two transmitting coils 102, we can draw two ellipsoids 501 and 502 using the two measured magnetic field strengths as shown in FIG. 5. The crossing line between the two ellipsoids is an oval shaped closed line 503 on a curved 2-dimensional plane, and the receiver 104 is located on the crossing line of the two ellipsoids 501 and 502. The crossing line 503 may be only using the magnitudes of the measured magnetic fields by the receiver 104, no orientation information is required. At each point on the crossing line, we can estimate the expected magnetic field vectors in the transmitter's coordinate frame (X, Y, Z), (E_(x1), E_(y1), E_(z1)) and (E_(x2), E_(y2), E_(z2)), using a physical model. We can also estimate the angle between the two estimated vectors, (E_(x1), E_(y1), E_(z1)) and (E_(x2), E_(y2), E_(z2)), at each point on the crossing line as follows:

$\begin{matrix} {\theta = {\arccos\left( \frac{{E_{x\; 1}E_{x\; 2}} + {E_{y\; 1}E_{y\; 2}} + {E_{z\; 1}E_{z\; 2}}}{\sqrt{E_{x\; 1}^{2} + E_{y\; 1}^{2} + {E_{z\; 1}^{2}\sqrt{E_{x\; 2}^{2} + E_{y\; 2}^{2} + E_{z\; 2}^{2}}}}} \right)}} & (3) \end{matrix}$

The receiver position may be found by comparing the estimated angle θ with the measured angle θ_(M) because the difference between the estimated angle and the measured angle |θ−θ_(M)| will be the minimum, ideally zero, at the receiver 104 position. This works because the angle between any two vectors remains the same when the coordinate frame rotates, and hence the calculated angle between the two estimated vectors in the transmitter's 104 coordinate frame (X, Y, Z) and the angle between the two measured vectors in the receiver's own coordinate frame (U, V, W) must be the same ideally at the position of the receiver 104.

Note that the position of the receiver 104 above is found without its orientation information. To find the orientation of the receiver 104 (α, β, γ) with respect to the transmitter 102 coordinate frame (X, Y, Z), we can use the estimated magnetic field vectors (E_(x1), E_(y1), E_(z1)) and (E_(x2), E_(y2), E_(z2)) at the found position and the measured magnetic field vectors (E_(u1), E_(v1), E_(w1)) and (E_(u2), E_(v2), E_(w2)). For example, we can estimate the rotation matrix for the rotation from (E_(x1), E_(y1), E_(z1)) to (E_(u1), E_(v1), E_(w1)), and/or from (E_(x2), E_(y2), E_(z2)) to (E_(u2), E_(v2), E_(w2)). Using the rotation matrix, we can estimate the orientation of the receiver (α, β, γ) with respect to the transmitter's coordinate frame (X, Y, Z).

FIG. 6 shows a simplified block diagram of the positioning process 600 using two transmitting coils. The process starts at stage 602 where the magnetic sensor 106 senses the transmitter 102 magnetic field vector in the receiver 104 coordinate frame. At stage 604 the envelope detector 115 (or alternatively the computing unit 118) detects the envelope of the magnetic field signals. At stage 606, the computing unit 118 calculates the magnetic field signal vectors in the receiver 104 coordinate fram using the maxima and minima of the envelope. At stage 608, the magnitudes of the magnetic field vectors are evaluated. At step 610, the position of the receiver 104 is determined using the magnitudes and angle of the expected (modeled) and measured values of the transmitting coil 102 field. At stage 612, coordinate correction is optionally applied to the position. At stage 614, the receiver 104 position is used to determine the magnetic field vectors at the receiver location in the transmitter coil's (X, Y, Z) coordinate frame. At step 616, the rotation matrix is determined to find the orientation of the receiver 104.

FIG. 7 shows an example implementation of the system 100 for determining the location and orientation of the receiver relative to the transmitters 102 using a distributed magnetic field model from the two transmitters 102. Use of the distributed model improves location accuracy significantly. FIG. 8 shows a process 800 for implementing the disclosed method. The process starts at stage 802 where the amplitudes from the three orthogonal coils in the magnetic sensor 106 are read. At stage 804, the envelope of the received signals is detected and the magnetic field vectors in the receiver coordinate system (u, v, w) are computed. At stage 808, the absolute magnetic field vectors from the two transmitter coils 102, along with the angle between the two vectors, is calculated using the dot product formula. At stage 810, the computing unit 118 checks the error between the magnetic model of the transmitter coils 102. The model is constructed by breaking the transmitter loop into smaller sections and applying Biot-Savart law to calculate the magnetic-filed vector at any given location (x,y,z) using it. To reduce the compute time, this calculation is done for just one loop of the coil 102 and the resultant field is multiplied be the total number of turns. If the error between the measured field values and the modeled values is not less than a predetermined minimum error, the process moves to stage 812. At stage 812, the expected magnetic field values for a plurality of positions around the estimated position are calculated. In one example, 27 corners are evaluated (x−Δx:Δx:x+Δx, y−Δy:Δy:y+Δy, z−Δz:Δz:z+Δz), where Δ is the step size. The Euclidean distance is then found between the expected magnetic-field value and the one calculated for the 27 corners. The corner with the least distance (out of 27) is selected as the new starting position (stage 814) and the process is repeated (returns to step 810) until the solution converges and the error is within the predetermined limit.

If the error from step 810 is within the predetermined limit, the process moves to stage 816, where the x/y/z step size is compared to a predetermined minimum. If the step size is at the minimum, the computing unit 118 outputs the estimated x,y,z position of the receiver 104 (stage 820). If not, the step size is reduced (stage 818) and the error is again evaluated (step 810).

At stage 822, The magnetic-field vector at the receiver 104 position (x, y, z) in the transmitter coil 102 co-ordinate system is determined. From the magnetic field vectors ({right arrow over (E)}₁ and {right arrow over (E)}_(z)) in the transmitter coil 102 co-ordinate system (which uses (X, Y, Z)) and its projection in the receiver 104 co-ordinate system (which uses (U, V, W)), the rotation or orientation angles are determined and output (stage 824).

In order to resolve potential problems with polarity ambiguity, the following method may be used in one embodiment. The receiver 104 can possibly be located in one of the four quadrants relative to the transmitter coils 102: (+X, +Y), (+X, −Y), (−X, +Y), (+X, +Y). The signals directly from the tri-axial magnetic sensor 106 (before low-pass filtering) are processed to determine the polarity. The following algorithm is used to find polarity (No rotation is assumed here: α=β=γ0, and w,coil >(u,coil+w,coil)):

1. If max(u,coil+w,coil)>max(w,coil), then X is positive, else X is negative

2. If max(v,coil+w,coil)>max(w,coil), then Y is positive, else Y is negative

3. If α≠0 or β≠0 or γ≠0, then angle correction needs to be applied based on the magnetic field vectors at estimated (x, y, z) location and then the above algorithm is reapplied.

This method works because, assuming α=β=γ=0, when the receiver position is shifted from one quadrant to another, the direction of flux lines entering the u, v coil (among the three tri-axial coils) changes, changing the amplitude sign. The w coil at the same time, always remains in one side of the coil and is hence used as a reference.

In another embodiment, a 3-Dimensional sensor (e.g., a compass+accelerometer) can be used to find out the rotation angle direction with respect to the transmitter 102 which can be used to detect the quadrant of the receiver 104. As only the sign of rotation is to be determined here with some computation, one of the sensors can be removed. E.g. if the transmitter coils 102 are laid flat on a table and the receiver 104 hovers above it, only pitch and roll angles are required to detect the correct quadrant of the receiver and hence the quadrant detection will be achieved only with an accelerometer.

Indoor RF transmission modalities can be heavily affected by channel characteristics, e.g., the structure of buildings. In various embodiments, frequencies <1 MHz are used for effective propagation through, e.g., walls, human bodies, and other features of indoor environments. Such frequencies have wavelengths in the tens of meters, so the receivers can operate in the near field of the transmitting antenna, and not in the far field. Therefore radiative effects do not need to be considered or compensated for, in various examples. Lower frequencies increase the antenna size and provide improved penetration of objects. In various embodiments using frequencies of 12 MHz or higher, position accuracy can be more affected by walls than at lower frequencies. However, frequencies of 12 MHz and above can be used, and advantageously still pass through human bodies.

In the disclosed embodiments, various low frequencies can be used since the electromagnetic spectrum is not heavily used at LF. Other users include ham radio operators. Multiple frequencies can be used for different transmitters, and receivers can include notch filters corresponding to specific transmitter frequencies to avoid interference.

Any of the computing units 118, the receiver 104, the magnetic sensor 106, the signal generator 110, the driver 112 may include one or more computer processors, memory, and data storage units for analyzing data and performing other analyses described herein, and related components. The processors can each include one or more microprocessors, microcontrollers, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), programmable logic devices (PLDs), programmable logic arrays (PLAs), programmable array logic devices (PALs), or digital signal processors (DSPs). The data storage unit can include or be communicatively connected with one or more processor-accessible memories configured to store information. The memories can be, e.g., within a chassis or as parts of a distributed system. The phrase “processor-accessible memory” is intended to include any data storage device to or from which processor 186 can transfer data, whether volatile or nonvolatile; removable or fixed; electronic, magnetic, optical, chemical, mechanical, or otherwise. Exemplary processor-accessible memories include but are not limited to: registers, floppy disks, hard disks, tapes, bar codes, Compact Discs, DVDs, read-only memories (ROM), erasable programmable read-only memories (EPROM, EEPROM, or Flash), and random-access memories (RAMs). One of the processor-accessible memories in the data storage system 140 can be a tangible non-transitory computer-readable storage medium, i.e., a non-transitory device or article of manufacture that participates in storing instructions that can be provided to processor for execution.

Various aspects described herein may be embodied as systems or methods. Accordingly, various aspects herein may take the form of an entirely hardware aspect, an entirely software aspect (including firmware, resident software, micro-code, etc.), or an aspect combining software and hardware aspects. These aspects can all generally be referred to herein as a “service,” “circuit,” “circuitry,” “module,” or “system.”

Furthermore, various aspects herein may be embodied as computer program products including computer readable program code stored on a tangible non-transitory computer readable medium. Such a medium can be manufactured as is conventional for such articles, e.g., by pressing a CD-ROM. The program code includes computer program instructions that can be loaded into the processor (and possibly also other processors), to cause functions, acts, or operational steps of various aspects herein to be performed by the processor. Computer program code for carrying out operations for various aspects described herein may be written in any combination of one or more programming language(s).

The invention is inclusive of combinations of the aspects described herein. References to “a particular aspect” or “embodiment” and the like refer to features that are present in at least one aspect of the invention. Separate references to “an aspect” (or “embodiment”) or “particular aspects” or the like do not necessarily refer to the same aspect or aspects; however, such aspects are not mutually exclusive, unless so indicated or as are readily apparent to one of skill in the art. The use of singular or plural in referring to “method” or “methods” and the like is not limiting. The word “or” is used in this disclosure in a non-exclusive sense, unless otherwise explicitly noted.

The invention has been described in detail with particular reference to certain preferred aspects thereof, but it will be understood that variations, combinations, and modifications can be effected by a person of ordinary skill in the art within the spirit and scope of the invention. 

1. A positioning system, comprising: a) two transmitting coils, each coil configured to transmit a periodic signal with a respective selected frequency during a positioning event, wherein the frequencies of the two signals transmitted by the two transmitting coils during the positioning event are different; b) a receiver including a sensing unit for measuring the magnetic field vectors produced by the two simultaneously transmitting coils; and c) a computing unit configured to use the measured magnetic field vectors to calculate the position and orientation of the receiver with respect to the transmitter's coordinate frame.
 2. The system according to claim 1, wherein the sensing unit includes a tri-axis magnetic sensor.
 3. The system according to claim 1, in which one or both of the transmitting coils are integrated into a mobile electronic device, and both the transmitting coils and sensing unit move simultaneously, and wherein the orientation of the transmitting coil(s) in the earth's coordinate system is provided to the computing unit in the receiver at real time.
 4. The system of claim 1, comprising a plurality of receivers which operate simultaneously and independently.
 5. The system according to claim 1, wherein the computing unit is integrated in the receiver.
 6. The system according to claim 1, wherein the computing unit is located remotely from the receiver, the receiver transmits the measured magnetic field vector in the receiver's own coordinate system to the computing unit through a wired or wireless channel.
 7. The system according to claim 1, wherein the magnetic sensor includes three planar coils oriented orthogonally to each other.
 8. The system according to claim 1, wherein the receiver comprises a plurality of tri-axis magnetic sensors for measuring the magnetic field of the transmitting coil.
 9. The system according to claim 1, wherein the receiver comprises a a solid-state compass to measure the receiver orientation in the earth's coordinate system, the receiver orientation is transmitted to the computing unit.
 10. The system according to claim 1, wherein the transmitting coils are integrated into a computing unit, the position data of the receiver is transmitted to the computing unit.
 11. The system according to claim 10, wherein the computing unit comprises at least one of a television, mobile phone, tablet computer, notebook computer, desktop computer, wearable device and a video gaming device.
 12. The system according to claim 1, wherein the receiver is integrated into the computing unit, allowing the position of the computing unit with respect to the transmitting coils to be determined.
 13. The system according to claim 1, wherein the receiver is configured as a stand-alone unit, the receiver sends the position and orientation data to the computing unit through a wired or wireless channel.
 14. The system according to claim 1, wherein the transmitting coils are configured to transmit a beacon signal, the beacon signal including a periodic signal portion for determining the receiver position and an auxiliary signal portion.
 15. The system according to claim 14, wherein the auxiliary signal portion includes at least one of coil identification information, coil orientation, transmitting signal frequency, transmitting coil size, and transmitting coil shape.
 16. The system according to claim 1, further comprising: a plurality of pairs of transmitting coils, each pair configured to transmit at a different set of frequencies than the other pairs; and a plurality of receivers, each of said receivers configured to receive signals from one of said pairs.
 17. The system according to claim 1, wherein the computing unit is configured to perform an initial estimate of the receiver position and orientation of the receiver, and then evaluate a plurality of positions around the initial estimated position.
 18. The system according to claim 17, wherein the computing unit is further configured to evaluate errors between measured field values for the plurality of positions and predicted field values.
 19. The system according to claim 18, the computing unit further configured to select a second estimated position from the plurality of positions, the second estimated position having the smallest field error compared to the remaining plurality of positions.
 20. A method of determining a position of a receiver in relation to a pair of transmitting coils, comprising: simultaneously transmitting a pair of periodic signals during a positioning event using the pair of transmitting coils, the periodic signals having different frequencies; using a receiver, sensing a magnetic field vector produced by the transmitting coils; using a computing device, estimating a position and orientation of the receiver with respect to the transmitter coils' coordinate system using the measured magnetic field vector from the two transmitter coils. 